Generating drug repositioning hypotheses based on integrating multiple aspects of drug similarity and disease similarity

ABSTRACT

Various embodiments predict drug-disease associations. In one embodiment, a plurality of disease similarity matrices and a plurality of disease similarity matrices are accessed. Each of the plurality of drug similarity matrices is associated with a different drug information source. Each of the plurality of disease similarity matrices is associated with a different disease information source. A known drug-disease association matrix is also accessed. The known drug-disease association matrix indicates if a given drug identified is known to treat a given disease. At least one drug-disease association prediction is generated based on the plurality of drug similarity matrices, the plurality of disease similarity matrices, and the known drug-disease association matrix. The at least one drug-disease association prediction identifies a previously unknown association between a given drug and a given disease, and a probability that the given disease is treatable by the given drug.

BACKGROUND

The present disclosure generally relates to drug repositioning, and moreparticularly relates to generating drug repositioning hypotheses basedon integrating multiple aspects of drug similarities and diseasesimilarities.

In response to the high cost and high risk associated with traditionalde novo drug discovery, investigation of potential additional uses forexisting drugs, also known as drug repositioning, has attractedincreasing attention from both the pharmaceutical industry and theresearch community. Drug repositioning presents a promising avenue foridentifying better and safer treatments without the full cost or timerequired for de novo drug development. Candidates for repositioning areusually either market drugs or drugs that have been discontinued inclinical trials for reasons other than safety concerns. Because thesafety profiles of these drugs are known, clinical trials foralternative indications are cheaper, potentially faster, and carry lessrisk than de novo drug development. Any newly identified indications canbe quickly evaluated from phase II clinical trials. Drug repositioningcan also greatly reduce drug discovery and development time.

BRIEF SUMMARY

In one embodiment, a method for predicting drug-disease associations isdisclosed. The method comprises accessing a plurality of diseasesimilarity matrices and a plurality of disease similarity matrices. Eachof the plurality of drug similarity matrices is associated with adifferent drug information source. Each of the plurality of diseasesimilarity matrices is associated with a different disease informationsource. A known drug-disease association matrix is also accessed. Theknown drug-disease association matrix indicates if a given drugidentified is known to treat a given disease. At least one drug-diseaseassociation prediction is generated based on the plurality of drugsimilarity matrices, the plurality of disease similarity matrices, andthe known drug-disease association matrix. The at least one drug-diseaseassociation prediction identifies a previously unknown associationbetween a given drug and a given disease, and a probability that thegiven disease is treatable by the given drug.

In another embodiment, an information processing system for predictingdrug-disease associations is disclosed. The information processingcomprises memory and at least one processor that is communicativelycoupled to the memory. A drug repositioning manager is communicativelycoupled to the memory and the at least one processor. The drugreposition manager configured to perform a method. The method comprisesaccessing a plurality of disease similarity matrices and a plurality ofdisease similarity matrices. Each of the plurality of drug similaritymatrices is associated with a different drug information source. Each ofthe plurality of disease similarity matrices is associated with adifferent disease information source. A known drug-disease associationmatrix is also accessed. The known drug-disease association matrixindicates if a given drug identified is known to treat a given disease.At least one drug-disease association prediction is generated based onthe plurality of drug similarity matrices, the plurality of diseasesimilarity matrices, and the known drug-disease association matrix. Theat least one drug-disease association prediction identifies a previouslyunknown association between a given drug and a given disease, and aprobability that the given disease is treatable by the given drug.

In yet another embodiment, a computer program product for predictingdrug-disease associations is disclosed is disclosed. The computerprogram product comprises a storage medium readable by a processingcircuit and storing instructions for execution by the processing circuitfor performing a method. The method comprises accessing a plurality ofdisease similarity matrices and a plurality of disease similaritymatrices. Each of the plurality of drug similarity matrices isassociated with a different drug information source. Each of theplurality of disease similarity matrices is associated with a differentdisease information source. A known drug-disease association matrix isalso accessed. The known drug-disease association matrix indicates if agiven drug identified is known to treat a given disease. At least onedrug-disease association prediction is generated based on the pluralityof drug similarity matrices, the plurality of disease similaritymatrices, and the known drug-disease association matrix. The at leastone drug-disease association prediction identifies a previously unknownassociation between a given drug and a given disease, and a probabilitythat the given disease is treatable by the given drug.

BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWINGS

The accompanying figures where like reference numerals refer toidentical or functionally similar elements throughout the separateviews, and which together with the detailed description below areincorporated in and form part of the specification, serve to furtherillustrate various embodiments and to explain various principles andadvantages all in accordance with the present disclosure, in which:

FIG. 1 is a block diagram illustrating one example of an operatingenvironment according to one embodiment of the present disclosure;

FIGS. 2-4 provide various examples of drug similarity matrices accordingto one embodiment of the present disclosure;

FIGS. 5-7 provide various examples of disease similarity matricesaccording to one embodiment of the present disclosure;

FIG. 8 is a graphical representation of generating drug repositioningpredictions/estimations according to one embodiment of the presentdisclosure;

FIG. 9 shows one example of a known drug-disease association matrixaccording to one embodiment of the present disclosure;

FIG. 10 shows one example of an algorithm for generating drugrepositioning predictions/estimations according to one embodiment of thepresent disclosure;

FIG. 11 shows one example of a drug cluster assignment matrix accordingto one embodiment of the present disclosure;

FIG. 12 shows one example of a disease cluster assignment matrixaccording to one embodiment of the present disclosure;

FIG. 13 shows one example of an estimated drug-disease associationmatrix according to one embodiment of the present disclosure;

FIG. 14 shows one example of an algorithm for performing a ProjectedGradient calculation according to one embodiment of the presentdisclosure;

FIG. 15 shows one example of an algorithm for performing an ImprovedProjected Gradient calculation according to one embodiment of thepresent disclosure;

FIG. 16 shows one example of a disease-drug cluster relationship matrixaccording to one embodiment of the present disclosure;

FIG. 17 is a graph showing the number of indicated diseases per drugaccording to one embodiment of the present disclosure;

FIG. 18 is a graph showing the number of drugs per disease according toone embodiment of the present disclosure;

FIG. 19 is a graph showing averaged ROC comparison of five drugrepositioning approaches generated from 50 runs of 10-foldcross-validation;

FIG. 20 is a graph showing the weights for various drug similaritysources according to one embodiment of the present disclosure;

FIG. 21 is a graph showing the weights for various disease similaritysources according to one embodiment of the present disclosure;

FIG. 22 is a table showing the top 10 drugs identified by one or moreembodiments for Alzheimer's Disease;

FIG. 23 is an operational flow diagram illustrating one example of aprocess for performing a drug repositioning task according to oneembodiment of the present disclosure; and

FIG. 24 is a block diagram illustrating one example of an informationprocessing system according to one embodiment of the present disclosure.

DETAILED DESCRIPTION

The inefficiency of pharmaceutical drug development with highexpenditure but low productivity has been widely discussed. Drugrepositioning, which is the process of finding additional indications(i.e., diseases) for existing drugs, presents a promising avenue foridentifying better and safer treatments without the full cost or timerequired for de novo drug development. Candidates for repositioning areusually either market drugs or drugs that have been discontinued inclinical trials for reasons other than safety concerns. Because thesafety profiles of these drugs are known, clinical trials foralternative indications are cheaper, potentially faster, and carry lessrisk than de novo drug development. Any newly identified indications canbe quickly evaluated from phase II clinical trials. Drug repositioningcan reduce drug discovery and development time from an average of 10-17years to potentially 3-12 years. Therefore, it is not surprising that inrecent years, new indications, new formulations, and new combinations ofpreviously marketed products accounted for more than 30% of the newmedicines that reach their first markets. Drug repositioning has drawnwidespread attention from the pharmaceutical industry, governmentagencies, and academic institutes. However, current successes in drugrepositioning have primarily been the result of serendipitous eventsbased on ad hoc clinical observation, unfocused screening, and “happyaccidents”. Comprehensive and rational approaches are urgently needed toexplore repositioning opportunities.

Accordingly, one or more embodiments provide a unified computationalframework for drug repositioning hypothesis generation by integratingmultiple Drug information sources and multiple Disease informationsources to facilitate drug Repositioning tasks (DDR). At least oneembodiment utilizes drug similarity network, disease similarity network,and known drug-disease associations to analyze potential associationsamong other unlinked drugs and diseases. Various types of druginformation (e.g., chemical structure, target protein, and side effects)and various types of disease information (e.g., phenotype, ontology, anddisease gene) are utilized by various embodiments for drug repositioninghypothesis generation. These embodiments are extensible and canincorporate additional types of drug/disease information sources.

Embodiments of the present disclosure are advantageous over conventionaldrug repositioning methods because they are able to predict additionaldrug-disease associations by considering both drug information anddisease information. In addition, various embodiments determine theninterpretable importance of different information sources during theprediction. Also, various embodiments discover the drug and diseasegroups as by-products such that the drugs or diseases within the samegroup are highly correlated with each other. This provides additionalinsights for targeted downstream investigations including clinicaltrials.

FIG. 1 shows one example of an operating environment 100 for generatingdrug repositioning hypotheses. In the example shown in FIG. 1, theoperating environment 100 comprises a plurality of informationprocessing systems 102, 104, 106, 107. Each of the informationprocessing systems 102, 104, 106, 107 is communicatively coupled to oneor more networks 108 comprising connections such as wire, wirelesscommunication links, and/or fiber optic cables. One or more of theinformation processing systems 102, 104, 107 provide information sources110, 112, 113 comprising drug data 114, disease data 116, and knowndrug-disease association data 117. Examples of drug data include (butare not limited to) drug name, drug manufacturer, drug chemicalstructure, drug target protein, drug side effects, and/or the like.Examples of disease data included (but are not limited to) disease name,disease phenotype, disease ontology, disease genes, and/or the like.Known drug-disease association data 117 comprises information such asdisease names and the known drugs that have been used or that arecurrently being used to treat each disease.

At least one of the information processing systems 106 comprises a drugrepositioning manager 118. The drug repositioning manager 118 comprisesa drug similarity calculator 120, a disease similarity calculator 122,and a drug repositioning hypothesis/prediction generator 124. The drugsimilarity calculator 120 generates drug similarity measures 126 forvarious drugs based on drug data 114 obtained from the informationsources 110. The disease similarity calculator 120 generates diseasesimilarity measures 128 for various diseases based on disease data 116obtained from the information sources 112. The drug repositioninghypothesis/prediction generator 124 predicts and generates drug-diseaseassociations 130 by considering both the generated drug and diseasesimilarity measures 126, 128. The methods, operations, and processesperformed by the prediction generator 124 are herein referred to as“DDR”. The drug repositioning manager 118 and its components arediscussed in greater detail below.

In one embodiment, the drug repositioning manager 118 automaticallyobtains the drug and disease data 114, 116 from the information sources110, 112. For example, the drug repositioning manager 118 canautomatically query (or perform a data pull operation) the informationsources 110, 112 for drug and disease data 114, 116 at predefinedintervals or based upon receiving a command from a user interacting withthe information processing system 106. In another example, the drug theinformation sources 110, 112 automatically push the drug and diseasedata 114, 116 to the repositioning manager 118 at predefined intervals,based upon the data 114, 116 being updated, and/or the like. Once drugand disease data 114, 116 is obtained, the drug and disease similaritycalculators 120, 122 calculate drug and similarity measures 124, 126,respectively.

In one embodiment, drug/disease similarities 124, 126 are utilized bythe drug repositioning manager 118 to quantify the degree of commoncharacteristics shared between pairs of drugs/diseases. For example, adrug or disease similarity calculated for a pair of drugs or diseases isa score that ranges from 0 to 1, with 0 representing the lowestsimilarity and 1 representing the highest similarity. It should be notedthat embodiments are not limited to these scores and otherrepresentations are applicable as well. The drug similarity calculator124 calculates various types of drug similarity measures including (butnot limited to) similarity measures based on chemical structures, targetproteins, and side effects. The disease similarity calculator 122calculates various types of disease similarity measures including (butnot limited to) similarities based on disease phenotypes, diseaseontology, and disease genes.

Drugs with similar chemical structures will likely carry out commontherapeutic functions and treat common diseases. Therefore, the drugsimilarity calculator 124 calculates a first drug pairwise similaritymeasure, D^(chem), based on a chemical structure fingerprintcorresponding to the substructures of the drugs. In one embodiment, the881 chemical substructures defined in the PubChem database are utilizedto calculate the D^(chem) similarity. In this embodiment, each drug d isrepresented by an n-dimensional binary profile h(d) (e.g., an881-dimensional binary profile) whose elements encode for the presenceor absence of each chemical substructure by 1 or 0, respectively. Thenthe pairwise chemical similarity between two drugs d and d′ is computedby the drug similarity calculator 120 as the Tanimoto coefficient oftheir chemical fingerprints:

$\begin{matrix}{{D_{d,d^{\prime}}^{chem} = \frac{{h(d)} \cdot {h\left( d^{\prime} \right)}}{{{h(d)}} + {{h\left( d^{\prime} \right)}} - {{h(d)} \cdot {h\left( d^{\prime} \right)}}}},} & \left( {{EQ}\mspace{14mu} 1} \right)\end{matrix}$

where |h(d)| and |h(d′)| are the counts of substructure fragments indrugs d and d′ respectively. The dot product h(d)·h(d′) represents thenumber of substructure fragments shared by two drugs. The drugsimilarity calculator 120 then generates an n×n drug similarity matrixD_(chem). FIG. 2 shows one example of this similarity matrix 200 whereeach element of the matrix 200 comprises the similarity measure/scorebetween two drugs based on their chemical structures. For example, FIG.2 shows that the matrix 200 includes an element 202 comprising thesimilarity measure of D₁₂ ^(chem) for drugs d₁ and d₂.

A second drug pairwise similarity measure calculated by the drugsimilarity calculator 124 is a target protein similarity measure,D^(target). A drug target is the protein in the human body whoseactivity is modified by a drug resulting in a desirable therapeuticeffect. Drugs sharing common targets often possess similar therapeuticfunction. After the drug repositioning manager 118 obtains drug data 114comprising target protein information the drug similarity calculator 124calculates the pairwise drug target similarity between drugs d and d′based on the average of sequence similarities of their target proteinsets according to:

$\begin{matrix}{{D_{d,d^{\prime}}^{target} = {\frac{1}{{{P(d)}}{{P\left( d^{\prime} \right)}}}{\sum\limits_{i = 1}^{{P{(d)}}}\; {\sum\limits_{j = 1}^{{P{(d^{\prime})}}}\; {{SW}\left( {{P_{i}(d)},{P_{j}\left( d^{\prime} \right)}} \right)}}}}},} & \left( {{EQ}\mspace{14mu} 2} \right)\end{matrix}$

where given a drug d, the drug similarity calculator 124 presents itstarget protein set as P(d); then |P(d)| is the size of the targetprotein set of drug d. The sequence similarity function of two proteinsSW is calculated by the drug similarity calculator 120 as aSmith-Waterman sequence alignment score. The drug similarity calculator120 then generates an n×n drug similarity matrix D_(target). FIG. 3shows one example of this similarity matrix 300 where each element ofthe matrix 300 comprises the similarity measure/score between two drugsbased on their target proteins. For example, FIG. 3 shows that thematrix 300 includes an element 302 comprising the similarity measure ofD₁₂ ^(target) for drugs d₁ and d₂.

A third drug pairwise similarity measure calculated by the drugsimilarity calculator 124 is a drug side effect similarity measure,D^(se). Drug side effects, or adverse drug reactions, indicate themalfunction by off-targets. Thus, side effects are useful to inferwhether two drugs share similar target proteins and treat similardiseases. Once the drug repositioning manager 118 obtains drug data 114comprising side effect information the drug similarity calculator 124represents each drug d by an y-dimensional binary side effect profilee(d) (e.g., a 4192-dimensional binary side effect profile e(d)) whoseelements encode for the presence or absence of each of the side effectkey words by 1 or 0 respectively. Then, the pairwise side effectsimilarity between two drugs d and d′ is computed by the drug similaritycalculator 120 as the Tanimoto coefficient of their side effectprofiles:

$\begin{matrix}{{D_{d,d^{\prime}}^{se} = \frac{{e(d)} \cdot {e\left( d^{\prime} \right)}}{{{e(d)}} + {{e\left( d^{\prime} \right)}} - {{e(d)} \cdot {e\left( d^{\prime} \right)}}}},} & \left( {{EQ}\mspace{14mu} 3} \right)\end{matrix}$

where |e(d)| and |e(d′)| are the counts of side effect keywords fordrugs d and d′ respectively. The dot product e(d)·e(d′) represents thenumber of side effects shared by two drugs. The drug similaritycalculator 120 then generates an n×n drug similarity matrix D_(se). FIG.4 shows one example of this similarity matrix 400 where each element ofthe matrix 400 comprises the similarity measure/score between two drugsbased on their side effects. For example, FIG. 4 shows that the matrix400 includes an element 402 comprising the similarity measure of D₁₂^(se) for drugs d₁ and d₂.

In one embodiment, the disease similarity calculator 126 calculates afirst pairwise disease similarity measure, S^(pheno), based on diseasephenotypes. Disease phenotypes indicate phenotypic abnormalitiesencountered in human diseases. After the drug repositioning manager 118obtains disease data 116 comprising drug phenotype information, thedisease similarity calculator 122 constructs a disease phenotypicsimilarity measure for two or more diseases by identifying thesimilarity between various terms associated with the diseases. Forexample, if the information source 112 is a knowledge base of humangenes and genetic disorders such as the Online Mendelian Inheritance inMan (OMIM), the disease similarity calculator 122 identifies thesimilarity between the Medical Subject Headings (MeSH) appearing in themedical description (“full text” and “clinical synopsis” fields) ofdiseases from the OMIM database. In this embodiment, each disease sobtained from the disease data 116 is represented by a K-dimensional (Kis the number of the terms) term feature vector in(s). Each entry in thefeature vector represents a term of interest (e.g., MeSH terms), and thecounts of the term found for disease s are the corresponding featurevalue. Then the pairwise disease phenotype similarity between twodiseases s and s′ is computed by the disease similarity calculator 122as the cosine of the angle between their feature vectors:

$\begin{matrix}{{S_{ss}^{pheno} = \frac{\sum\limits_{i = 1}^{K}\; {{m(s)}_{i}{m\left( s^{\prime} \right)}_{i}}}{\sqrt{\sum\limits_{i = 1}^{K}\; {m^{2}(s)}_{i}}\sqrt{\sum\limits_{i = 1}^{K}\; {m^{2}\left( s^{\prime} \right)}_{i}}}},} & \left( {{EQ}\mspace{14mu} 4} \right)\end{matrix}$

where m(s), denotes the i-th entry of the feature vector m(s). Thedisease similarity calculator 122 then generates an n×n diseasesimilarity matrix S_(pheno). FIG. 5 shows one example of this similaritymatrix 500 where each element of the matrix 500 comprises the similaritymeasure/score between two diseases based on their phenotypes. Forexample, FIG. 5 shows that the matrix 500 includes an element 502comprising the similarity measure of S₁₂ ^(pheno) for diseases s₁ ands₂.

A second pairwise disease similarity measure calculated by the diseasesimilarity calculator 122 is a disease ontology similarity measure,S^(do). The drug repositioning manager 118 obtains disease data 116comprising disease ontology information form an information source 112such as (but not limited to) the Disease Ontology (DO). The DiseaseOntology (DO) is an open source ontological description of human diseasethat is organized from a clinical perspective of disease etiology andlocation. The terms in DO are disease names or disease-related conceptsand are organized in a directed acyclic graph (DAG). Two linked diseasesin DO are in an “is-a” relationship, which means one disease is asubtype of the other linked disease, and the lower a disease is in theDO hierarchy, the more specific the disease term is. The diseasesimilarity calculator 122 utilizes the obtained disease data 116 tocalculate the semantic similarity between any pair of the diseases. Inone embodiment, for a disease term s in disease data 116, theprobability that the term is used in disease annotations is estimated asp_(s), which is the number of disease term s or its descendants in thedisease data 116 divided by the total number of disease terms in thedisease data 116. Then the semantic similarity of two diseases s and s′is defined as the information content of their lowest common ancestorby:

$\begin{matrix}{{S_{{ss}^{\prime}}^{do} = {{- \log}\mspace{11mu} {\min\limits_{x \in {C{({s,s^{\prime}})}}}p_{x}}}},} & \left( {{EQ}\mspace{14mu} 5} \right)\end{matrix}$

where C(s,s′) is the set of all common ancestors of diseases s and s′.The disease similarity calculator 122 then generates an n×n diseasesimilarity matrix S_(do). FIG. 6 shows one example of this similaritymatrix 600 where each element of the matrix 600 comprises the similaritymeasure/score between two diseases based on their ontology information.For example, FIG. 6 shows that the matrix 600 includes an element 602comprising the similarity measure of S₁₂ ^(do) for diseases s₁ and s₂.

A third disease similarity measure, S^(gene), calculated by the diseasesimilarity calculator 122 is based on disease genes. Disease-causingaberrations in the normal function of a gene define that gene as adisease gene. In this embodiment, the drug repositioning manager 118obtains disease data 116 comprising disease gene information. Forexample, the drug repositioning manager 118 collects all disease genesfor each disease from “phenotype-gene relationships” field from the OMIMdatabase. The disease similarity calculator 122 calculates the pairwisedisease similarity between diseases s and s′ based on the average ofsequence similarities of their disease gene sets as defined by:

$\begin{matrix}{{S_{{ss}^{\prime}}^{gene} = {\frac{1}{{{G(s)}{}{G\left( s^{\prime} \right)}}}{\sum\limits_{i = 1}^{{{G{(s)}}}}\; {\sum\limits_{j = 1}^{{G{(s^{\prime})}}}{S\; {W\left( {{G_{i}(s)},{G_{j}\left( s^{\prime} \right)}} \right)}}}}}},} & \left( {{EQ}\mspace{14mu} 6} \right)\end{matrix}$

where given a disease s, the disease similarity calculator 126 presentsits disease gene set as G(s); then |G(s)| is the size of the diseasegene set of disease s. The sequence similarity function of two diseasegenes SW, in one embodiment, is calculated by the disease similaritycalculator 122 as a Smith-Waterman sequence alignment score. The diseasesimilarity calculator 122 then generates an n×n disease similaritymatrix S_(gene). FIG. 7 shows one example of this similarity matrix 700where each element of the matrix 700 comprises the similaritymeasure/score between two diseases based on their genes. For example,FIG. 7 shows that the matrix 700 includes an element 702 comprising thesimilarity measure of S₁₂ ^(gene) for diseases s₁ and s₂.

The drug and disease similarity matrices discussed above and knowndrug-disease associations 117 are inputted into the drug repositioningprediction generator 124. The drug repositioning prediction generator124 utilizes these inputs to generate one or more drug repositioningpredictions 130, latent drug groupings, latent disease groupings, and animportance weighting for information sources. For example, FIG. 8 showsa graphical representation 800 of an overall process for generating oneor more drug repositioning predictions 130 according to at least oneembodiment of the present disclosure. In the example shown in FIG. 8,the drug repositioning prediction generator 124 takes as input aplurality of drug similarity matrices (networks) D₁ 802, D₂ 804, andD_(n) 806; a plurality of disease similarity matrices (networks) S₁ 808,S₂ 810, and S_(n) 812; and a known/observed drug-disease associationmatrix R 814. The known/observed drug-disease association matrix R 814is generated by the drug repositioning prediction generator 124 based onobtained drug-disease association data 113. For example, the predictiongenerator 124 analyze and parses the drug-disease association data 113and identifies which drugs are being used (or have been previously used)to treat a given disease. The prediction generator 124 then generates amatrix 814 comprising these associations.

The known/observed drug-disease association matrix R 814 is a matrixwith each row representing a given drug and each column representing agiven disease (or vice versa). Each element in the matrix indicateswhether the drug-disease combination has a known association. Forexample, FIG. 9 shows one example of a known/observed drug-diseaseassociation matrix R 900 generated by the prediction generator 124. Inthis example, each row 902 corresponds to a drug d and each column 904corresponds to a disease s. If an element 906 of a given row/columncomprise a value of “1”, this indicates that the associated drug anddisease have a known association (i.e., the drug is used or has beenused to treat the disease). If an element 906 of a given row/columncomprise a value of “0”, this indicates that the associated drug anddisease do not have a known association (i.e., the drug is not currentlybeing used or has not been previously used to treat the disease). Itshould be noted that other values/characters besides “1” and “0” can beutilized to indicate a known drug-disease association or the absencethereof.

Returning now to FIG. 8, the prediction generator 124 utilizes the drugsimilarity matrices D₁ 802, D₂ 804, and D_(n) 806; plurality of diseasesimilarity matrices S₁ 808, S₂ 810, and S_(n) 812; and theknown/observed drug-disease association matrix R 814 to learn adrug/disease grouping matrix U or V, an estimated drug similarity matrixUU^(T) 816, an estimated disease similarity matrix VV^(T) 818, anestimated drug-disease association matrix Θ 820, and an importancefactor ω 822 or π 824 of different drug/disease information sources. Theestimated drug-disease association matrix Θ comprises new drug-diseaseassociations identified by the prediction generator 124. Stateddifferently, the prediction generator 124 identifies one or more drugsthat can be utilized to treat a given disease(es) where the identifieddrug(s) is not currently being used or has not been previously used totreat the given disease(s).

In particular, assume there are n information sources to measure drugsimilarity, in information sources to measure disease similarity, and atotal of K_(d) information sources to measure the drug similarities, anda total of K_(s) sources to measure the disease similarities. Let D_(k)∈

^(n×n) be a drug similarity matrix measured on the k-th informationsource. Similarly, let S_(l)∈

^(m×m) be a disease similarity matrix measured on the l-th informationsource. Let U∈

^(n×C) _(D) be a latent drug grouping matrix with C_(D) being the numberof drug groups, and U_(ij) indicating the possibility that the i-th drugbelongs to the j-th drug cluster. Let V∈

^(m×C) _(s) be a latent disease grouping matrix with C_(S) the number ofdisease groups, and V_(ij) indicating the possibility that the i-thdisease belongs to the j-th disease cluster. Let R∈

^(n×m) be an observed (i.e., known) drug-disease association matrix withR_(ij)=1 if the association between the i-th drug and j-th disease isobserved, and R_(ij)=0 otherwise.

Based on the above, the prediction generator 124 integrates multipledrug similarities, multiple disease similarities, and known drug-diseaseassociations to calculate a global estimation on the entire drug-diseasenetwork including the intrinsic drug similarity, intrinsic diseasesimilarity, as well as drug-disease associations. The predictiongenerator 124 formulates such a network estimation problem as aconstrained nonlinear optimization problem. For example, the predictiongenerator 124 analyzes the drug-disease network comprising the drug anddisease matrices generated by the prediction generator 124 by minimizingthe following objective:

J=J ₀+λ₁ J ₁+λ₂ J ₂   (EQ 7),

where λ₁ and λ₂ are user-defined weighting factors for J₁ and J₂,respectively, and indicate how much weight is to be given to theirrespective part of the objective.

The objective in EQ 7 has three parts: J₀, J₁ and J₂. J₀ is thereconstruction loss of observed drug-disease associations and is definedas follows:

J ₀ =∥Θ−UΛV ^(T)∥_(F) ²   (EQ 8).

Here, Θ∈

^(n×m) is the estimated dense version of R, Λ∈

^(C) _(D) ^(×C) _(S) encodes the relationship between drug clusters anddisease clusters, and ∥·∥_(F) denotes Frobenius norm of a matrix.

J₁ is the reconstruction loss of drug similarities and is defined asfollows:

J ₁=Σ_(k=1) ^(K) ^(d) ω_(k) ∥D _(k) −UU ^(T)∥_(F) ²+δ₁∥∈∥₂ ²   (EQ 9).

Here, the estimated drug similarity matrix is UU^(T), and ω∈

^(K) _(d) ^(×1) is the non-negative weight vector when aggregating thereconstruction loss on different drug information sources. UU^(T) ismatrix that integrates the drug similarity matrices 802, 804, 806generated by the prediction manager 124 based on heterogeneousinformation sources. The L₂ norm regularization is added to avoidtrivial solution and δ₁≧0 is the tradeoff parameter.

J₂ is the reconstruction loss of disease similarities and is defined asfollows:

J ₂=Σ_(l=1) ^(k) ^(s) π_(l) ∥S _(l) −VV ^(T)∥_(F) ²+δ₂∥π∥₂ ²   (EQ 10).

Here, the estimated disease similarity matrix is VV^(T), and π∈

^(K) _(s) ^(×1) is the non-negative weight vector when aggregating thereconstruction loss on different disease information sources. VV^(T) ismatrix that integrates the disease similarity matrices 808, 810, 812generated by the prediction manager 124 based on heterogeneousinformation sources. The L₂ norm regularization is added for the samereasons as in equation (EQ 9).

Combining the above, the prediction generator 124 resolves the followingoptimization problem:

min_(U,V,Λ,Θ,ω,π)J   (EQ 11),

subject to U≧0, V≧0, Λ≧0, ω≧0, ω^(T)1=1, π^(T)1=1, P_(Ω)(Θ)=P_(Ω)(R),where Ω is the set of indices of the observed associations, and P_(Ω) isthe projection operator on obtaining the entries of a matrix indexed bythe indices in Ω. Thus, the constraint P_(Ω)(Θ)=P_(Ω)(R) restricts theestimated drug-disease associations should include the ones that arealready observed. Note that to enhance the interpretability of thelearned model, U, V, and Λ, in one embodiment, are non-negative and ωand π are in simplexes. Table 1 below lists the various notations andsymbols discussed above.

TABLE 1 Notation Size Meaning D_(k) n × n The k-th drug similaritymatrix S_(l) m × m The l-th disease similarity matrix U n × C_(D) Drugcluster assignment matrix V m × C_(S) Disease cluster assignment matrixΛ C_(D) × C_(S) Drug-disease cluster relationship matrix R n × mObserved drug-disease association matrix Θ n × m Densified estimation ofR ω K_(d) × 1 Drug similarity weight vector π K_(s) × 1 Diseasesimilarity weight vector

Since there are multiple groups of variables involved in theoptimization problem (EQ 11), the prediction generator 124 utilizes anefficient solution based on the Block Coordinate Descent (BCD) strategy.Therefore, in one embodiment, the prediction generator 124 solves thedifferent groups of variables alternatively until convergence. In oneembodiment, convergence occurs when the reconstruction losses J₀, J₁,and J₂ no longer decrease. At each iteration, the prediction generator124 solves the optimization problem with respect to one group ofvariables with all other groups of variables fixed.

The following is a more detailed discussion on how the predictiongenerator 124 iteratively solves the optimization problem of EQ 11 byintegrating multiple drug similarities, multiple disease similarities,and known drug-disease associations. As discussed above, this DDRprocess allows the prediction generator 124 to achieve a globalestimation on the entire input drug-disease network including newdrug-disease associations, intrinsic drug similarity, and intrinsicdisease similarity. FIG. 10 shows one example of an algorithm 1000illustrating an overall process performed by the prediction generator124 to identify new drug-disease associations, the interpretableimportance of different information sources, and drug and diseasegroups. In one embodiment, the prediction generator 124 is programmed toperform the operations shown in the algorithm 1000.

The prediction generator 124 utilizes the drug matrices {D_(k)}_(k=1)^(K) ^(d) , the disease matrices {S_(l)}_(l=1) ^(K) ^(s) , and the knowndrug-disease association matrix R as inputs to perform the operationsshown in FIG. 10. In addition, FIG. 10 shows that the user-definedweighting factors λ₁ and λ₂, the tradeoff parameters δ₁ and δ₂, theK_(d) drug information sources, and the K_(s) disease informationsources are to be greater or equal to 0. Once the prediction generator124 has received/generated its input it initializes various variables inthe objective function EQ 10. For example, the prediction generator 124initializes ω=(1/K_(d))1∈

^(K) ^(d) ^(×1) and π=(1/K_(s))1∈

^(K) ^(s) ^(×1). In other words, the importance factors ω for each ofthe drug information sources (e.g., drug chemical structure, drug targetprotein, drug side effects) are initially set equal to each other, andthe importance factors π for each of the disease information sources(e.g., disease name, disease phenotype, disease ontology, disease genes)are initially set equal to each other.

The prediction generator 124 initializes the disease clusterrelationship matrix Λ by populating the matrix with random values. Theprediction generator 124 initializes the drug cluster assignment matrixU and the disease cluster assignment matrix V by performing SymmetricNon-negative Factorization on {tilde over (D)}=Σ_(k=1) ^(K) ^(d)ω_(k)D_(k) and {tilde over (S)}=Σ_(l=1) ^(K) _(s)π_(l)S₁. One method ofSymmetric Non-negative Factorization that is applicable for initializingU and Vis given by Wang et al., “Community Discovery Using NonnegativeMatrix Factorization”, Data Min Knowl Discov 22: 493-521 (2011), whichis hereby incorporated by reference in its entirety. FIGS. 11 and 12show examples of a drug cluster assignment matrix U 1100 and a diseasecluster assignment matrix V 1200, respectively, after being initialized.In the example shown in FIG. 11, each row 1102 of the matrix 1100corresponds to a given drug d and each column 1104 corresponds to agiven drug group/class C_(D). In one embodiment, the number of druggroups/classes is user defined. An element 1106 of a given row/columnwithin the drug cluster assignment matrix U 1100 indicates theprobability that the dug represented by the given row belongs to thedrug group/class represented by the given column, with the sum of theprobabilities in a given row being equal to 1. For example, FIG. 11shows that there is a 10% probability that drug d₁ belongs to the drugclass C_(D1), a 40% probability that drug d₁ belongs to the drug classC_(D2), a 10% probability that drug d₁ belongs to the drug class C_(D3),and a 20% probability that drug d₁ belongs to the drug class C_(D1).Therefore, drug d₁ is assigned to drug class C_(D2) since it has thehighest probability associated therewith, e.g., 40%.

In the example shown in FIG. 12, each row 1202 of the matrix 1200corresponds to a given disease s and each column 1204 corresponds to agiven disease group/class C_(S). In one embodiment, the number ofdisease groups/classes is user defined. An element 1206 of a givenrow/column within the disease cluster assignment matrix V 1200 indicatesthe probability that the disease represented by the given row belongs tothe disease group/class represented by the given column, with the sum ofthe probabilities in a given row being equal to 1. For example, FIG. 12shows that there is a 5% probability that disease s₁ belongs to thedisease class C_(S1), a 1% probability that disease s₁ belongs to thedisease class C_(S2), a 2% probability that disease s₁ belongs to thedisease class C_(S3), and a 25% probability that disease s₁ belongs tothe disease class C_(Sn). Therefore, disease s₁ is assigned to drugclass C_(sn), since it has the highest probability associated therewith,e.g., 25%.

After the initialization process discussed above, the predictiongenerator 124 iteratively calculates the estimated drug-diseaseassociation matrix Θ (the densified estimation of R); the drugsimilarity weight vector ω; the disease similarity weight vector π; thedrug-disease cluster relationship matrix Λ; the drug cluster assignmentmatrix U; and the disease cluster assignment matrix V.

The prediction generator 124 first calculates the estimated drug-diseaseassociation matrix Θ, which is a densified estimation of R. In oneembodiment, the prediction generator 124 calculates Θ according to:

min_(Θ) ∥Θ−W∥ _(F) ², subject to P _(Ω)(Θ)=P _(Ω)(R)   (EQ 12),

where W=UΛV^(T). This is a constrained Euclidean projection, and can bedecoupled for every element in Θ. Each sub-problem has a closed formsolution. By aggregating all solutions together, the predictiongenerator 124 obtains the matrix form representation of the solution as:

Θ*=P _(Ω) ^(c)(W)+P _(Ω)(R)   (EQ 13),

where Ω^(c) is the complementary index set for Ω.

FIG. 13 shows one example of an estimated drug-disease associationmatrix Θ. The estimated drug-disease association matrix comprises newdrug-disease associations calculated/identified by the predictiongenerator 124 based on the processes discussed above. In particular, Θcomprises new drug-disease associations that were not previously foundin the known drug-disease association data or generated matrix. In thisexample, each row 1302 of the matrix 1300 corresponds to a drug d andeach column 1304 corresponds to a disease s. If the value of eachelement 1306 in a given row/column indicates the probability that givendrug can be used to treat the given disease. A value of 0 indicates thatthere is no likelihood of the drug treating the disease. A value of 1indicates that there is a 100% likelihood of the drug treating thedisease.

When compared to the known/observed drug-disease association matrix R ofFIG. 9, the matrix 1300 of FIG. 13 comprises at least two newdrug-disease associations/predictions. In particular, the matrix 1300shows that drug d₂ and disease s₁ have an association with a 90%probability that drug d₂ can treat disease s_(i). The matrix 1300 alsoshows that drug d_(n) and disease s₂ have an association with a 75.2%probability that drug d_(n) can treat disease s₁. FIG. 9 shows thatthese drug/disease combinations were not previously associated with oneanother. Stated differently, based on the processes discussed above, theprediction generator 124 determined that drug d₃ can potentially beutilized to treat disease s₁ and drug d_(n) can potentially be utilizedto treat disease s₃ even though these drugs have not been previouslyused or known to treat these diseases.

Once the prediction generator 124 has calculated Θ, the predictiongenerator 124 then calculates ω. It should be noted that the process forπ is similar to ω. Therefore, the following discussion is alsoapplicable to calculating π (where ω is replaced with π, D is replacedwith S, and U is replaced with V). In one embodiment, the predictiongenerator 124 calculates ω according to:

min_(ω)Σ_(k=1) ^(K) ^(d) ω_(k) ∥D _(k)−Σ∥_(F) ²−δ₁∥ω∥₂ ², subject toω≧0, ω^(T)1=1   (EQ 14),

where Σ=UU^(T).

Let

A=[∥D ₁−Σ∥_(F) ² , ∥D ₂−Σ∥_(F) ² , . . . , ∥D _(K) _(d) −Σ∥_(F) ²]^(T)  (EQ 15).

Then, EQ 17 can be reformulated as:

$\begin{matrix}{{{\min_{\omega}{\delta_{1}{{\omega - {\frac{1}{2\; \delta_{1}}A}}}_{2}^{2}}} + c},{{{subject}\mspace{14mu} {to}\mspace{14mu} \omega} \geq 0},{{\omega^{T}1} = 1},} & \left( {{EQ}\mspace{14mu} 16} \right)\end{matrix}$

where c is some constant irrelevant to ω. This is a standard Euclideanprojection problem and can be efficiently solved using various methodssuch as that discussed in Chen Y et al. “Projection Onto A Simplex:,arXiv:1101.6081 (2011), which is hereby incorporated by reference in itsentirety.

Once ω and π have been calculated the prediction generator 124calculates the drug-disease cluster relationship matrix Λ according to:

min_(Λ) ∥Θ−UΛV ^(T)∥_(F) ², subject to Λ≧0   (EQ 17).

EQ 17 is a non-negative quadratic optimization problem and is solved bythe prediction generator 124 utilizing Projected Gradient Descent (PGD).In order to obtain the gradient of the objective of problem (EQ 17) withrespect to Λ, it is expanded as:

J _(Λ) =∥Θ−UΛV ^(T)∥_(f) ² =tr(Θ−UΛV ^(T))^(T)(Θ−UΛV ^(T))=tr(VΛ ^(T) U^(T) UΛV ^(T))-31 2tr(Θ^(T) UΛV ^(T))+c,

where c is some constant irrelevant to Λ. Then the prediction generator124 can derive the gradient J_(Λ) with respect to Λ as

$\begin{matrix}{\frac{\partial J_{\Lambda}}{\partial\Lambda} = {{2\; U^{T}U\; \Lambda \; V^{T}V} - {2\; U^{T}\Theta \; {V.}}}} & \left( {{EQ}\mspace{14mu} 18} \right)\end{matrix}$

In more detail, a non-negative projection operator P⁻(A) is introducedas:

$\left( {P_{+}(A)} \right)_{ij} = \left\{ {\begin{matrix}A_{ij} & {{{if}\mspace{14mu} A_{ij}} \geq 0} \\0 & {otherwise}\end{matrix}.} \right.$

Then, one Projected Gradient (PG) method that can be performed by theprediction generator 124 for solving the problem

$\min\limits_{A \geq 0}\mspace{14mu} {f(A)}$

can be presented as shown in the algorithm 1400 of FIG. 14. FIG. 14shows that this PG method requires 0<β<1, 0<σ<1, initialization A⁽⁰⁾,while ensuring) A⁽⁰⁾≧0. Then, for k=1, 2, . . . , the followingcalculations are performed:

A^((k))=P⁻(A^((k−1))−α_(k) ∇f(A^((k−1)))) where α_(k)=β^(t) ^(k) , andt_(k) is the first nonnegative integer for which

f(A ^((k)))−f(A ^((k−1)))≦σ∇f(A ^((k−1)))^(T)(A ^((k)) −A ^((k−1)))  (EQ 19).

Here, the condition in EQ 19 ensures the sufficient decrease of thefunction value per iteration, and this rule of determining the stepsizeis usually referred to as the Armijo rule.

However, the Armijo rule is usually time consuming, thus the predictiongenerator 124 utilizes the improved PG method shown in the algorithm1500 of FIG. 15. In particular, this PG method requires 0<β<1, 0<σ<1,Initialization A⁽⁰⁾, and α₀=1 while ensuring A⁽⁰⁾≧0. The for k=1, 2, . .. , the prediction generator 124 performs the following calculations.First, the prediction generator 124 assigns α_(k)=α_(k−1). If α_(k)satisfies the condition in EQ 19, the prediction generator 124repeatedly increases it by α_(k)←α_(k)/β until either α_(k) does notsatisfy the condition in EQ 19 or A(α_(k)/β)=A(α_(k)). Otherwise, theprediction generator 124 repeatedly decreases α_(k) by α_(k)←α_(k). βuntil α_(k) satisfies the condition in EQ 19. The prediction generator124 sets A^((k))=P₊(A^((k−1))−α_(k)∇f(A^((k−1)))).

As a result of the above operations, the prediction generator 124outputs a resulting drug-disease cluster relationship matrix Λ, which isa latent matrix. FIG. 16 shows one example of this matrix where each row1602 of the matrix 1600 represents a drug cluster from the drug clusterassignment matrix U and each column 1604 represents a disease clusterfrom the disease cluster assignment matrix V. Each element 1606 of thematrix 1600 identifies a degree of association between the given drugcluster and the given disease cluster. In the example shown in FIG. 16,drug group C_(D1) has a stronger association (0.5) with C_(S3) than withC_(S2) (0.2).

Once the drug-disease cluster relationship matrix A has been generated,the prediction generator 124 calculates the drug and disease clusterassignment matrices U and V. The prediction generator 124 calculates thedrug cluster assignment matrix U according to:

$\begin{matrix}{{{\min_{U}{{\Theta - {U\; \Lambda \; V^{T}}}}_{F}^{2}} + {\lambda_{1}{\sum\limits_{k = 1}^{K_{d}}\; {\omega_{k}{{D_{k} - {U\; U^{T}}}}_{F}^{2}}}}},{{{subject}\mspace{14mu} {to}\mspace{11mu} U} \geq 0.}} & \left( {{EQ}\mspace{14mu} 20} \right)\end{matrix}$

The objective of EQ 20 can be expanded as:

${J_{U} = {{{{\Theta - {U\; \Lambda \; V^{T}}}}_{F}^{2} + {\lambda_{1}{\sum\limits_{k = 1}^{K_{d}}\; {\omega_{k}{{D_{k} - {U\; U^{T}}}}_{F}^{2}}}}} = {{{tr}\left( {U\; \Lambda \; V^{T}V\; \Lambda^{T}U^{T}} \right)} - {2\; {{tr}\left( {U\; \Lambda \; V^{T}\Theta^{T}} \right)}} - {2\; \lambda_{1}{{tr}\left( {U^{T}\overset{\sim}{D}U} \right)}} + {\lambda_{1}{{tr}\left( {U^{T}{UU}^{T}U} \right)}} + c}}},$

where {tilde over (D)}=Σ_(k=1) ^(K) ^(c) ω_(k)D_(k) and c is someconstant irrelevant to U. Then the gradient of J_(U) with respect to Uis:

$\begin{matrix}{\frac{\partial J_{U}}{\partial U} = {{2\; U\; \Lambda \; V^{T}V\; \Lambda^{T}} - {2\; \Theta \; V\; \Lambda^{T}} - {2\; \lambda_{1}\overset{\sim}{D}\; U} + {4\; \lambda_{1}U\; U^{T}{U.}}}} & \left( {{EQ}\mspace{14mu} 21} \right)\end{matrix}$

The prediction generator 124 calculates the disease cluster assignmentmatrix V according to:

$\begin{matrix}{{{\min_{V}{{\Theta - {U\; \Lambda \; V^{T}}}}_{F}^{2}} + {\lambda_{2}{\sum\limits_{l = 1}^{K_{s}}\; {\pi_{l}{{S_{l} - {V\; V^{T}}}}_{F}^{2}}}}},{{{subject}\mspace{14mu} {to}\mspace{14mu} V} \geq 0.}} & \left( {{EQ}\mspace{14mu} 22} \right)\end{matrix}$

Similarly the objective of EQ 22 can be expanded as:

${J_{V} = {{{{\Theta - {U\; \Lambda \; V^{T}}}}_{F}^{2} + {\lambda_{2}{\sum\limits_{l = 1}^{K_{s}}\; {\pi_{l}{{S_{l} - {V\; V^{T}}}}_{F}^{2}}}}} = {{{tr}\left( {V\; {\Lambda \;}^{T}U^{T}U\; \Lambda \; V^{T}} \right)} - {2\; {{tr}\left( {V^{T}\Theta^{T}U\; \Lambda} \right)}} - {2\; \lambda_{2}{{tr}\left( {V^{T}\overset{\sim}{S}V} \right)}} + {\lambda_{2}{{tr}\left( {V^{T}V\; V^{T}V} \right)}} + c}}},$

where {tilde over (S)}=Σ_(l=1) ^(K) ^(s) π_(l)S_(l) and c is someconstant irrelevant to V. Then the gradient of J_(V) with respect to Vis:

$\begin{matrix}{\frac{\partial J_{V}}{\partial V} = {{2\; V\; \Lambda^{T}U^{T}U\; \Lambda} - {2\; \Theta^{T}U\; \Lambda} - \; {2\lambda_{2}\overset{\sim}{S\;}V} + {4\; \lambda_{2}V\; V^{T}{V.}}}} & \left( {{EQ}\mspace{14mu} 23} \right)\end{matrix}$

The prediction generator 124 then outputs U and V matrices similar tothose shown in FIGS. 11 and 12.

Once the prediction generator 124 has calculated Λ, Θ, ε, π, U, and V itcalculates J₀ (the reconstruction loss of observed drug-diseaseassociations) according to EQ 8, J₁ (the reconstruction loss of drugsimilarities) according to EQ 9, and J₂ (the reconstruction loss ofdisease similarities) according to EQ 10 to determine if a convergencehas occurred. If so, the prediction generator 124 outputs the optimizedΘ, ω, π, U, and V. If convergence has not occurred, the predictiongenerator 124 performs another iteration of the process shown in FIG. 10using the values for Λ, Θ, ω, π, U, and V calculated in the previousiteration. This process continues until convergence is reached.

The computational cost involved in each BCD iteration includes thefollowing. When updating Θ, the main computation happens at calculatingUΛV^(T), which takes O(nK_(d)K_(s)+nmK_(s)) time. When updating ω, themain computation happens at calculating UU^(T), which takes O(n²K_(d))time. The Euclidean projection takes O(K_(d) log K_(d)) time. Whenupdating π, the main computation happens at calculating VV^(T), whichtakes O(m²K_(s)) time. The Euclidean projection takes O(K_(s) log K_(s))time. Updating A involves PGD iterations. We just need to evaluateU^(T)ΘV once, which takes O(K_(d)nm+K_(d)K_(s)m) time. At each iterationevaluating U^(T)UΛV^(T)V takes O(K_(d) ²K_(s)+K_(s) ²K_(d)) time (asUU^(T) and VV^(T) are already computed), and evaluating the J_(Λ) takesO(K_(d) ²K_(s)) time. Updating U involves PGD iterations. ΘVΛ^(T) andΛV^(T)VΛ^(T) only need to be evaluated once, which takes O(nK_(d)K_(s))and O(K_(d)K_(s) ²+K_(s)K_(d) ²) time. At each iteration evaluatingUΛV^(T)VΛ^(T) takes O(nK_(d) ²) time, {tilde over (D)}U takesO(n²K_(d)), UU^(T)U takes O(nk_(d) ²+n²K_(d)) time, and evaluating J_(U)takes O(nK_(d) ²) time. Updating V involves PGD iterations. Λ^(T)U^(T)UΛand Θ^(T)UΛ only need to be evaluated once once, which takesO(nK_(d)K_(s)+nK_(d) ²) and O(mnK_(d)+mK_(d)K_(s)) time. At eachiteration evaluating VΛ^(T)U^(T)UΛ takes O(mK_(s) ²) time, {tilde over(S)}V takes O(m²K_(s)) time, VV^(T)V takes O(mK_(s) ²+K_(s)m²) time, andevaluating J_(V) takes O(mK_(s) ²) time. Adding up everything together,and considering the fact that max(K_(d), K_(s))<<min(m,n), the roughcomputational complexity is O(R{tilde over (r)}mn), where R is thenumber of BCD iterations, and {tilde over (r)} is the average PGDiterations when updating Λ, U, and V.

The following discussion presents various experimental results ofvarious DDR methods performed by the prediction generator 124 on a drugrepositioning task. In one experiment performed by the inventors, abenchmark dataset was used to test the performance of the predictiongenerator 124 using a community standard. This dataset was extractedfrom the National Drug File-Reference Terminology (NDF-RT) produced bythe U.S. Department of Veterans Affairs, Veterans Health Administration(VHA). The dataset spanned 3,250 treatment associations between 799drugs and 719 diseases. Drug information was considered from three datasources: chemical structure, target protein, and side effect. Thus,three 799×799 matrices were used to represent drug similarities between799 drugs from different perspectives. Similarly, disease informationwas considered from three data sources: disease phenotype, diseaseontology, and disease gene. Thus, three 719×719 matrices were used torepresent disease similarities between 719 human diseases from differentperspectives. The presence or absence of known associations betweendrugs and diseases was denoted by 1 or 0 respectively. Thus, a 799×719matrix R was used to represent the known drug-disease associations. Thestatistics of the known drug-disease associations from knowndrug-disease association data is plotted in FIGS. 17 and 18. In thatdataset, most of the drugs (75%) treat <5 diseases; 18% of drugs treat 5to 10 diseases; and only 7% of drugs treat >10 diseases (FIGS. 17 and18). Although the disease hypertension has 78 related drugs, 80% ofdiseases have only <5 drugs; 10% of diseases have 5-10 drugs; and theremaining 10% of diseases have >10 drugs.

A 10-fold cross-validation scheme was used to evaluate drugrepositioning approaches. To ensure the validity of the test cases, allthe associations involved with 10% of the drugs in each fold were heldout, rather than holding out associations directly. To obtain robustresults, 50 independent cross-validation runs were performed, in each ofwhich a different random partition of dataset to 10 parts was used. Inthe comparisons, five drug repositioning methods were considered. Thefirst method was the DDR method of one or more embodiments using SimpleAverage. This method only considers reconstruction loss of observeddrug-disease associations (i.e., J₀ of objective formula (EQ 7), andassumes each drug/disease source was equally informative. Thus, thismethod uses the average of drug/disease similarity matrices as theintegrated drug/disease similarity.

The second method was the DDR method of one or more embodiments withWeighted Drug Similarity. This method considers reconstruction losses ofobserved drug-disease associations and drug similarities (i.e., J₀ andJ₁ in objective formula (EQ 7)). This method uses the average of diseasesimilarity matrices as integrated disease similarity, and automaticallylearns drug similarity weight vector (ω) based on the contributions ofdrug information sources to the prediction. The third method was the DDRmethod of one or more embodiments with Weighted Disease Similarity. Thismethod considers reconstruction losses of observed drug-diseaseassociations and disease similarities (i.e., J₀ and J₂ in objectiveformula (EQ 7)). This method uses the average of drug similaritymatrices as integrated drug similarity, and automatically learns diseasesimilarity weight vector (π) based on the contributions of diseaseinformation sources to the prediction.

The fourth method was the DDR method of one or more embodiments withWeighted Drug and Disease Similarities. This method considers allreconstruction losses proposed in the paper (i.e., formula (EQ 7) as awhole). This method automatically learns drug similarity weight vector(ω) and disease similarity weight vector (π) together based on thecontributions of drug and disease information sources to the prediction.The fifth method was PREDICT, which uses un-weighted geometric mean ofpairs of drug-drug and disease-disease similarity measures to constructclassification features and subsequently learns a logistic regressionclassifier that distinguishes between true and false drug-diseaseassociations. PREDICT could not provide weight for each drug/diseaseinformation source. The PREDICT method is further discussed in Gottliebet al., “PREDICT: A Method For Inferring Novel Drug Indications WithApplication To Personalized Medicine”. Mol Syst Biol 2011; 7:496. FIG.19 shows the averaged ROC curves of 50 runs of the cross-validation fordifferent methods based on the experiment.

FIG. 19 shows that the DDR framework of one or more embodiments iseffective for drug repositioning tasks. Without consideringreconstruction loss of any similarity measure, DDR using Simple Averageobtains an averaged AUC score of 0.7985. When considering weighted drugsimilarity (i.e., reconstruction loss of drug similarities) or weighteddisease similarity (i.e., reconstruction loss of disease similarities),DDRs obtain averaged AUC scores of 0.8508 or 0.8366 respectively. In theexperiment, drug-based optimization (i.e., DDR with Weighted DrugSimilarity) obtains a higher AUC score than disease-based optimization(i.e., DDR with Weighted Disease Similarity). This could be partiallyexplained with the following reason. The 799 drugs that were studied aremarketed medications, which usually have rich and precisepharmacological data; thus drug-based optimization might be preferred inthis case. For novel drugs or clinical candidates, disease-basedoptimization might be preferred to overcome missing knowledge in thepharmacology of a drug (e.g., additional targets, unknown side effect).When considering weighted drug similarity and weighted diseasesimilarity together, DDR obtain the highest averaged AUC score (0.8700).The observation indicates that drug-based optimization and disease-basedoptimization could be complementary, and computational drugrepositioning tasks should optimize both drug similarity and diseasesimilarity. Another observation is PREDICT with All Drug and DiseaseSimilarities is less accurate than DDR.

One advantageous characteristic of the DDR method performed by theprediction generator 124 is that it provides interpretable importance ofdifferent information sources based on their contributions to theprediction. The i-th element of drug/disease weight vector w/itcorresponds to the i-th drug/disease data sources. Since ω/π wasconstrained to be in a simplex in problem formula (EQ 11), the sum ofall elements of ω/π is 1. Obtained from DDR with Weighted Drug andDisease Similarities, the averaged DDR weights of each data source andtheir standard deviations during the cross-validation experiments areplotted in FIGS. 20 and 21. For drug data sources, chemical structureobtains averaged weight of 0.2744, target protein obtains averagedweight of 0.2295, and side effect obtains a much higher averaged weightof 0.4961 (FIG. 20). This can be partially explained with the followingreasons. Chemical structure and target protein sources focus on drug'smolecular mechanism of action (MOA) from a genotypic perspective.However, the pre-clinical outcomes based on MOA often do not correlatewell with therapeutic efficacy in drug development. It is estimated thatof all compounds effective in cell assays, only 30% of them could workin animals. Even worse, only 5% of them could work in humans. Sideeffects are generated when drugs bind to off-targets, which perturbunexpected metabolic or signaling pathways. For marketed drugs, whichhave relatively complete side effect profiles, side effect informationfrom clinical patients may be seen as valuable read-outs of drug effectsdirectly on human bodies (i.e., with less translational problems). Thus,side effects could serve as a promising perspective for drugrepositioning. For disease data sources, phenotype obtains averagedweight of 0.4248, disease ontology obtains averaged weight of 0.3958,and disease gene obtains a lower averaged weight of 0.1794 (FIG. 21).The lower weight of disease gene data source may be due to the fact thatthe gap between phenotype (human disease) and genotype (human gene) istoo large, and the known associations between diseases and genes(obtained from OMIM) are incomplete.

The inventors also performed an additional leave-disease-out experimentto demonstrate the capability of DDR of one or more embodiments onuncovering drug-disease associations and predicting novel drugcandidates for each disease. To ensure the validity of the test cases,all the known drug-disease associations were held out with the testeddisease. The validation setting mimics a real-world setting: oncerare/unknown diseases without any treatment information arise, acomputational drug repositioning method should provide potential drugsbased on characteristics (e.g. phenotypes, related genes) of the newdiseases and the existing drug/disease similarities. In the experiment,each disease i was alternatively left out and the DDR (consideredweighted drug and disease similarities) process was performed by theprediction generator 124. More specifically, all elements in the i-thcolumn of matrix R were set to 0. This R was used along withdrug/disease similarity matrices as inputs of to the predictiongenerator 124. Then, the i-th column of the densified estimated matrix Θwas used as the drug prediction scores for the disease i. In this way,prediction scores were obtained for all possible associations betweenthe 799 drugs and 719 diseases.

As an example, treatment predictions for Alzheimer's disease (AD) wereanalyzed. For the six drugs which are known to treat AD, the predictiongenerator 124 assigned scores of 0.7091 to Selegiline, 0.6745 toValproic Acid, 0.6348 to Galantamine, 0.5675 to Donepezil, 0.5571 toTacrine, and 0.5233 to Rivastigmine, which are significantly larger thanthose of the other 793 drugs (mean and standard deviation are0.1565±0.1628). FIG. 22 shows the top 10 drugs predicted for AD by theprediction generator 124, where an “*” denotes that the drug is knownand approved to treat the disease. Of the 10 drugs, only three(Selegiline, Valproic Acid, and Galantamine) appear in the knowndrug-disease association list. The remaining 7 predicted drugs (alongwith other high-ranked ones in the leave-disease-out experiment) cah beconsidered as drug repositioning candidates for AD. Some predictions areexplainable and supported by clinical evidence from ClinicalTrials.gov(i.e., pharmaceutical investigators have been aware of the associations,which are still in the experimental stages).

FIG. 23 is an operational flow diagrams illustrating one example of aprocess for predicting drug-disease associations. The operational flowdiagram of FIG. 23 beings at step 2302 and flows directly to step 2304.The drug repositioning manger 118, at step 2304, accesses a plurality ofdrug similarity matrices. Each of the plurality of drug similaritymatrices is associted with a different drug information source. The drugrepositioning manger 118, at step 2306, accesses a plurality of diseasesimilarity matrices. Each of the plurality of disease similaritymatrices is associated with a different disease information source. Thedrug repositioning manger 118, at step 2308, also accesses a knowndrug-disease association matrix. The known drug-disease associationmatrix indicating if a given drug identified is known to treat a givendisease.

The drug repositioning manger 118, at step 2310, generates at least onedrug-disease association prediction based on the plurality of drugsimilarity matrices, the plurality of disease similarity matrices, andthe known drug-disease association matrix. The at least one drug-diseaseassociation prediction identifying a previously unknown associationbetween a given drug and a given disease, and a probability that thegiven disease is treatable by the given drug. The drug repositioningmanger 118, at step 2312, stores the at least one drug-diseaseassociation prediction for presentation to a user via a user interface.The control flow exits at step 2314.

Referring now to FIG. 24, this figure is a block diagram illustrating aninformation processing system that can be utilized in variousembodiments of the present disclosure. The information processing system2402 is based upon a suitably configured processing system configured toimplement one or more embodiments of the present disclosure. Anysuitably configured processing system can be used as the informationprocessing system 2402 in embodiments of the present disclosure. Inanother embodiment, the information processing system 2402 is a specialpurpose information processing system configured to perform one or moreembodiments discussed above. The components of the informationprocessing system 2402 can include, but are not limited to, one or moreprocessors or processing units 2404, a system memory 2406, and a bus2408 that couples various system components including the system memory2406 to the processor 2404.

The bus 2408 represents one or more of any of several types of busstructures, including a memory bus or memory controller, a peripheralbus, an accelerated graphics port, and a processor or local bus usingany of a variety of bus architectures. By way of example, and notlimitation, such architectures include Industry Standard Architecture(ISA) bus, Micro Channel Architecture (MCA) bus, Enhanced ISA (EISA)bus, Video Electronics Standards Association (VESA) local bus, andPeripheral Component Interconnects (PCI) bus.

Although not shown in FIG. 24, the main memory 2406 includes at leastthe drug repositioning manager 118 and its components discussed abovewith respect to FIG. 1. Each of these components can reside within theprocessor 2404, or be a separate hardware component. The system memory2406 can also include computer system readable media in the form ofvolatile memory, such as random access memory (RAM) 2410 and/or cachememory 2412. The information processing system 2402 can further includeother removable/non-removable, volatile/non-volatile computer systemstorage media. By way of example only, a storage system 2414 can beprovided for reading from and writing to a non-removable or removable,non-volatile media such as one or more solid state disks and/or magneticmedia (typically called a “hard drive”). A magnetic disk drive forreading from and writing to a removable, non-volatile magnetic disk(e.g., a “floppy disk”), and an optical disk drive for reading from orwriting to a removable, non-volatile optical disk such as a CD-ROM,DVD-ROM or other optical media can be provided. In such instances, eachcan be connected to the bus 2408 by one or more data media interfaces.The memory 2406 can include at least one program product having a set ofprogram modules that are configured to carry out the functions of anembodiment of the present disclosure.

Program/utility 2416, having a set of program modules 2418, may bestored in memory 2406 by way of example, and not limitation, as well asan operating system, one or more application programs, other programmodules, and program data. Each of the operating system, one or moreapplication programs, other program modules, and program data or somecombination thereof, may include an implementation of a networkingenvironment. Program modules 2418 generally carry out the functionsand/or methodologies of embodiments of the present disclosure.

The information processing system 2402 can also communicate with one ormore external devices 2420 such as a keyboard, a pointing device, adisplay 2422, etc.; one or more devices that enable a user to interactwith the information processing system 2402; and/or any devices (e.g.,network card, modem, etc.) that enable computer system/server 2402 tocommunicate with one or more other computing devices. Such communicationcan occur via I/O interfaces 2424. Still yet, the information processingsystem 2402 can communicate with one or more networks such as a localarea network (LAN), a general wide area network (WAN), and/or a publicnetwork (e.g., the Internet) via network adapter 2426. As depicted, thenetwork adapter 2426 communicates with the other components ofinformation processing system 2402 via the bus 2408. Other hardwareand/or software components can also be used in conjunction with theinformation processing system 2402. Examples include, but are notlimited to: microcode, device drivers, redundant processing units,external disk drive arrays, RAID systems, tape drives, and data archivalstorage systems.

As will be appreciated by one skilled in the art, aspects of the presentinvention may be a system, a method, and/or a computer program product.The computer program product may include a computer readable storagemedium (or media) having computer readable program instructions thereonfor causing a processor to carry out aspects of the present invention.

The computer readable storage medium can be a tangible device that canretain and store instructions for use by an instruction executiondevice. The computer readable storage medium may be, for example, but isnot limited to, an electronic storage device, a magnetic storage device,an optical storage device, an electromagnetic storage device, asemiconductor storage device, or any suitable combination of theforegoing. A non-exhaustive list of more specific examples of thecomputer readable storage medium includes the following: a portablecomputer diskette, a hard disk, a random access memory (RAM), aread-only memory (ROM), an erasable programmable read-only memory (EPROMor Flash memory), a static random access memory (SRAM), a portablecompact disc read-only memory (CD-ROM), a digital versatile disk (DVD),a memory stick, a floppy disk, a mechanically encoded device such aspunch-cards or raised structures in a groove having instructionsrecorded thereon, and any suitable combination of the foregoing. Acomputer readable storage medium, as used herein, is not to be construedas being transitory signals per se, such as radio waves or other freelypropagating electromagnetic waves, electromagnetic waves propagatingthrough a waveguide or other transmission media (e.g., light pulsespassing through a fiber-optic cable), or electrical signals transmittedthrough a wire.

Computer readable program instructions described herein can bedownloaded to respective computing/processing devices from a computerreadable storage medium or to an external computer or external storagedevice via a network, for example, the Internet, a local area network, awide area network and/or a wireless network. The network may comprisecopper transmission cables, optical transmission fibers, wirelesstransmission, routers, firewalls, switches, gateway computers, and/oredge servers. A network adapter card or network interface in eachcomputing/processing device receives computer readable programinstructions from the network and forwards the computer readable programinstructions for storage in a computer readable storage medium withinthe respective computing/processing device.

Computer readable program instructions for carrying out operations ofthe present invention may be assembler instructions,instruction-set-architecture (ISA) instructions, machine instructions,machine dependent instructions, microcode, firmware instructions,state-setting data, or either source code or object code written in anycombination of one or more programming languages, including an objectoriented programming language such as Smalltalk, C++ or the like, andconventional procedural programming languages, such as the “C”programming language or similar programming languages. The computerreadable program instructions may execute entirely on the user'scomputer, partly on the user's computer, as a stand-alone softwarepackage, partly on the user's computer and partly on a remote computeror entirely on the remote computer or server. In the latter scenario,the remote computer may be connected to the user's computer through anytype of network, including a local area network (LAN) or a wide areanetwork (WAN), or the connection may be made to an external computer(for example, through the Internet using an Internet Service Provider).In some embodiments, electronic circuitry including, for example,programmable logic circuitry, field-programmable gate arrays (FPGA), orprogrammable logic arrays (PLA) may execute the computer readableprogram instructions by utilizing state information of the computerreadable program instructions to personalize the electronic circuitry,in order to perform aspects of the present invention.

Aspects of the present invention are described herein with reference toflowchart illustrations and/or block diagrams of methods, apparatus(systems), and computer program products according to embodiments of theinvention. It will be understood that each block of the flowchartillustrations and/or block diagrams, and combinations of blocks in theflowchart illustrations and/or block diagrams, can be implemented bycomputer readable program instructions.

These computer readable program instructions may be provided to aprocessor of a general purpose computer, special purpose computer, orother programmable data processing apparatus to produce a machine, suchthat the instructions, which execute via the processor of the computeror other programmable data processing apparatus, create means forimplementing the functions/acts specified in the flowchart and/or blockdiagram block or blocks. These computer readable program instructionsmay also be stored in a computer readable storage medium that can directa computer, a programmable data processing apparatus, and/or otherdevices to function in a particular manner, such that the computerreadable storage medium having instructions stored therein comprises anarticle of manufacture including instructions which implement aspects ofthe function/act specified in the flowchart and/or block diagram blockor blocks.

The computer readable program instructions may also be loaded onto acomputer, other programmable data processing apparatus, or other deviceto cause a series of operational steps to be performed on the computer,other programmable apparatus or other device to produce a computerimplemented process, such that the instructions which execute on thecomputer, other programmable apparatus, or other device implement thefunctions/acts specified in the flowchart and/or block diagram block orblocks.

The flowchart and block diagrams in the Figures illustrate thearchitecture, functionality, and operation of possible implementationsof systems, methods, and computer program products according to variousembodiments of the present invention. In this regard, each block in theflowchart or block diagrams may represent a module, segment, or portionof instructions, which comprises one or more executable instructions forimplementing the specified logical function(s). In some alternativeimplementations, the functions noted in the block may occur out of theorder noted in the figures. For example, two blocks shown in successionmay, in fact, be executed substantially concurrently, or the blocks maysometimes be executed in the reverse order, depending upon thefunctionality involved. It will also be noted that each block of theblock diagrams and/or flowchart illustration, and combinations of blocksin the block diagrams and/or flowchart illustration, can be implementedby special purpose hardware-based systems that perform the specifiedfunctions or acts or carry out combinations of special purpose hardwareand computer instructions.

The terminology used herein is for the purpose of describing particularembodiments only and is not intended to be limiting of the invention. Asused herein, the singular forms “a”, “an” and “the” are intended toinclude the plural forms as well, unless the context clearly indicatesotherwise. It will be further understood that the terms “comprises”and/or “comprising,” when used in this specification, specify thepresence of stated features, integers, steps, operations, elements,and/or components, but do not preclude the presence or addition of oneor more other features, integers, steps, operations, elements,components, and/or groups thereof.

The description of the present invention has been presented for purposesof illustration and description, but is not intended to be exhaustive orlimited to the invention in the form disclosed. Many modifications andvariations will be apparent to those of ordinary skill in the artwithout departing from the scope and spirit of the invention. Theembodiment was chosen and described in order to best explain theprinciples of the invention and the practical application, and to enableothers of ordinary skill in the art to understand the invention forvarious embodiments with various modifications as are suited to theparticular use contemplated.

1-10. (canceled)
 11. An information processing system for predictingdrug-disease associations, the information processing comprising:memory; and at least one processor communicatively coupled to thememory; and a drug repositioning manager communicatively coupled to thememory and the at least one processor, the drug reposition managerconfigured to perform a method comprising: accessing a plurality of drugsimilarity matrices, wherein each of the plurality of drug similaritymatrices is associated with a different drug information source;accessing a plurality of disease similarity matrices, wherein each ofthe plurality of disease similarity matrices is associated with adifferent disease information source; accessing a known drug-diseaseassociation matrix, the known drug-disease association matrix indicatingif a given drug identified is known to treat a given disease; generatingat least one drug-disease association prediction based on the pluralityof drug similarity matrices, the plurality of disease similaritymatrices, and the known drug-disease association matrix, the at leastone drug-disease association prediction identifying a previously unknownassociation between a given drug and a given disease, and a probabilitythat the given disease is treatable by the given drug.
 12. Theinformation processing system of claim 11, wherein generating the atleast one drug-disease association prediction comprises: analyzing theplurality of drug similarity matrices, the plurality of diseasesimilarity matrices, and the known drug-disease association matrix byminimizing an objective defined as:J=J ₀+λ₁ J ₁+λ₂ J ₂, where J₀ is a reconstruction loss of observeddrug-disease associations defined as: J₀=∥Θ−UΛV^(T)∥_(F) ², where Θ isan estimated drug-disease association matrix comprising the at least onedrug-disease association prediction, U is a drug cluster assignmentmatrix, Λ is a drug-disease cluster relationship matrix, V is a diseasecluster assignment matrix, T indicates a transpose, and ∥·∥_(F) denotesFrobenius norm of a matrix, where J₁ is a reconstruction loss of drugsimilarities defined as: J₁=Σ_(k=1) ^(K) ^(d) ω_(k)∥D_(k)−UU^(T)∥_(F)²+δ₁∥ω∥₂ ², where K_(d) is a plurality of drug information sourcesassociated with the plurality of drug similarity matrices, ω is animportance factor assigned to a given drug information source in theplurality of drug information sources, D_(k) is one of the plurality ofdrug similarity matrices, and δ is a tradeoff parameter, J₂ is areconstruction loss of drug similarities defined as: J₂=Σ_(l=1) ^(K)^(s) π_(l)∥S_(l)−VV^(T)∥_(F) ²+δ₂∥π∥₂ ², where K_(s) is a plurality ofdisease information sources associated with the plurality of diseasesimilarity matrices, π is an importance factor assigned to a givendisease information source in the plurality of disease informationsources, and S_(l) is one of the plurality of disease similaritymatrices, and δ is a tradeoff parameter, and where λ is a user-definedweight.
 13. The information processing system of claim 12, whereingenerating the at least one drug-disease association prediction furthercomprises: iteratively calculating the estimated drug-diseaseassociation matrix Θ, each drug information source importance factor ω,each disease information source importance factor π, the drug-diseasecluster relationship matrix Λ, the drug cluster assignment matrix U, andthe disease cluster assignment matrix V until the objective isminimized.
 14. The information processing system of claim 13, where at afirst iteration ω is initialized as ω=(1/K_(d))1∈

^(K) _(d) ^(×1), π it is initialized as π=(1/K_(s))1∈

^(K) _(s) ^(×1), Λ is initialized with random values, U is initializedby performing Symmetric Nonnegative Matrix Factorization on {tilde over(D)}=Σ_(k=1) ^(K) ^(d) ω_(k)D_(k), and V is initialized by performingSymmetric Nonnegative Matrix Factorization on {tilde over (S)}=Σ_(l=1)^(k) ^(s) π_(l)S_(l).
 15. The information processing system of claim 14,wherein at each iteration: the estimated drug-disease association matrixΘ is calculated according to: min_(Θ)∥Θ−W∥_(F) ², subject toP₁₀₆(Θ)=P_(Ω)(R), where W=UΛV^(T), Ω is a set of indices of observedassociations in R, and P_(Ω) is a projection operator on obtainingentries of a matrix indexed by the indices in Ω, the drug informationsource importance factor ω is calculated according to: min_(ω)Σ_(k=1)^(k) ^(d) ω_(k)∥D_(k)−Σ∥_(F) ²+δ₁∥ω∥₂ ², subject to ω≧0, ω^(T)1=1, whereΣ=UU^(T). the disease information source importance factor π iscalculated according to: min_(π)Σ_(k=1) ^(K) ^(s) π_(l)∥S_(l)=Σ∥_(F)²+δ₁∥π∥₂ ², subject to π≧0, π^(T)1=1, where Σ=VV^(T), and thedrug-disease cluster relationship matrix Λ is calculated according to:min_(Λ)∥Θ−UΛV^(T)∥_(F) ², subject to Λ≧0, the drug cluster assignmentmatrix U is calculated according to:${{\min_{U}{{\Theta - {U\; \Lambda \; V^{T}}}}_{F}^{2}} + {\lambda_{1}{\sum\limits_{k = 1}^{K_{d}}\; {\omega_{k}{{D_{k} - {U\; U^{T}}}}_{F}^{2}}}}},$subject to U≧0, and the disease cluster assignment matrix V iscalculated according to:${{\min_{V}{{\Theta - {U\; \Lambda \; V^{T}}}}_{F}^{2}} + {\lambda_{2}{\sum\limits_{l = 1}^{K_{s}}\; {\pi_{l}{{S_{l} - {V\; V^{T}}}}_{F}^{2}}}}},$subject to U≧0.
 16. A computer program product for predictingdrug-disease associations, the computer program product comprising: astorage medium readable by a processing circuit and storing instructionsfor execution by the processing circuit for performing a methodcomprising: accessing a plurality of drug similarity matrices, whereineach of the plurality of drug similarity matrices is associated with adifferent drug information source; accessing a plurality of diseasesimilarity matrices, wherein each of the plurality of disease similaritymatrices is associated with a different disease information source;accessing a known drug-disease association matrix, the knowndrug-disease association matrix indicating if a given drug identified isknown to treat a given disease; generating at least one drug-diseaseassociation prediction based on the plurality of drug similaritymatrices, the plurality of disease similarity matrices, and the knowndrug-disease association matrix, the at least one drug-diseaseassociation prediction identifying a previously unknown associationbetween a given drug and a given disease, and a probability that thegiven disease is treatable by the given drug.
 17. The computer programproduct of claim 16, wherein generating the at least one drug-diseaseassociation prediction comprises: analyzing the plurality of drugsimilarity matrices, the plurality of disease similarity matrices, andthe known drug-disease association matrix by minimizing an objectivedefined as:J=J ₀+λ₁ J ₁+λ₂ J ₂ where J₀ is a reconstruction loss of observeddrug-disease associations defined as: J₀=∥Θ−UΛV^(T)∥_(F) ², where Θ isan estimated drug-disease association matrix comprising the at least onedrug-disease association prediction, U is a drug cluster assignmentmatrix, Λ is a drug-disease cluster relationship matrix, V is a diseasecluster assignment matrix, T indicates a transpose, and ∥·∥_(F) denotesFrobenius norm of a matrix, where J₁ is a reconstruction loss of drugsimilarities defined as: J₁=Σ_(k=1) ^(K) ^(d) ω_(k)∥D_(k)−UU^(T)∥_(F)²+δ₁∥ω∥₂ ², where K_(d) is a plurality of drug information sourcesassociated with the plurality of drug similarity matrices, ω is animportance factor assigned to a given drug information source in theplurality of drug information sources, D_(k) is one of the plurality ofdrug similarity matrices, and δ is a tradeoff parameter, J₂ is areconstruction loss of drug similarities defined as: J₂=Σ_(l=1) ^(K)^(s) π_(l)∥S_(l)−VV^(T)∥_(F) ²+δ₂∥π∥₂ ², where K_(s) is a plurality ofdisease information sources associated with the plurality of diseasesimilarity matrices, π is an importance factor assigned to a givendisease information source in the plurality of disease informationsources, and S_(l) is one of the plurality of disease similaritymatrices, and δ is a tradeoff parameter, and where λ is a user-definedweight.
 18. The computer program product of claim 17, wherein generatingthe at least one drug-disease association prediction further comprises:iteratively calculating the estimated drug-disease association matrix Θ,each drug information source importance factor ω, each diseaseinformation source importance factor π, the drug-disease clusterrelationship matrix Λ, the drug cluster assignment matrix U, and thedisease cluster assignment matrix V until the objective is minimized.19. The computer program product of claim 18, where at a first iterationω is initialized as ω=(1/K_(d))1∈

^(K) _(d) ^(×1), π it is initialized as π=(1/K_(s))1∈

^(K) _(s) ^(×1), Λ is initialized with random values, U is initializedby performing Symmetric Nonnegative Matrix Factorization on {tilde over(D)}=Σ_(k=1) ^(K) ^(d) ω_(k)D_(k), and Vis initialized by performingSymmetric Nonnegative Matrix Factorization on {tilde over (S)}=Σ_(l=1)^(K) ^(s) π_(l)S_(l).
 20. The computer program product of claim 19,wherein at each iteration: the estimated drug-disease association matrixΘ is calculated according to: min_(Θ)∥Θ−W∥_(F) ², subject toP_(Ω)(Θ)=P_(Ω)(R), where W=UΛV^(T), Ω is a set of indices of observedassociations in R, and P_(Ω) is a projection operator on obtainingentries of a matrix indexed by the indices in Ω, the drug informationsource importance factor ω is calculated according to: min_(ω)Σ_(k=1)^(K) ^(d) ω_(k)∥D_(k)−Σ∥_(F) ²+δ₁∥ω∥₂ ², subject to ω≧0, ω^(T)1=1, whereΣ=UU^(T). the disease information source importance factor π iscalculated according to: min_(π)Σ_(k=1) ^(K) ^(s) π_(l)∥S_(l)−Σ∥_(F)²+δ₁∥π∥₂ ², subject to π≧0, π^(T)1=1, where Σ=VV^(T), and thedrug-disease cluster relationship matrix Λ is calculated according to:min_(Λ)∥Θ−UΛV^(T)∥_(F) ², subject to Λ≧0, the drug cluster assignmentmatrix U is calculated according to:${{\min_{U}{{\Theta - {U\; \Lambda \; V^{T}}}}_{F}^{2}} + {\lambda_{1}{\sum\limits_{k = 1}^{K_{d}}\; {\omega_{k}{{D_{k} - {U\; U^{T}}}}_{F}^{2}}}}},$subject to U≧0, and the disease cluster assignment matrix V iscalculated according to:${{\min_{V}{{\Theta - {U\; \Lambda \; V^{T}}}}_{F}^{2}} + {\lambda_{2}{\sum\limits_{l = 1}^{K_{s}}\; {\pi_{l}{{S_{l} - {V\; V^{T}}}}_{F}^{2}}}}},$subject to U≧0.